Why does "one-night stand" mean sex?

What does the word stand mean in this phrase?

From NOAD:

one-night stand noun 1 informal (also one-nighter) a sexual relationship lasting only one night. • a person with whom one has such a relationship. 2 a single performance of a play or show in a particular place.

The etymology is from the "play or show" meaning and the word probably comes from "stand" used in the military sense, as a confrontation:

• an act of holding one's ground against or halting to resist an opposing force : Custer's legendary last stand

The OED says s.v. "stand":

e. Theatr. Each of the halts made on a tour to give performances; the place at which a halt is made; the performance itself; transf., esp. in one-night stand n. at one-night adj. Special uses.

So the "stand" is the stopping place on a theatrical tour. The one-night stand is a place where the show is performed for only one night. Nothing to do with fighting.